Abstract
Our aim here is to study periodicity properties of the integral trajectories of the Hamilton vector field of a given pseudodifferential symbol p, lying in energy-level sets of the kind p -1(E), E ∈ [E 1,E 1], with which we shall associate the action integral. This will be done in the next section. In section 11.2 we shall then give a crash introduction to the Maslov index of a periodic trajectory, with the aim of enabling the reader to compute it in the cases of interest for us. In the notes to the chapter we shall also give a rapid overview of the reason why one needs this symplectic invariant, that will systematically appear in Chapter 12.
Keywords
- Symplectic Form
- Symmetric Bilinear Form
- Periodic Trajectory
- Maslov Index
- Lagrangian Manifold
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Parmeggiani, A. (2010). Energy-Levels, Dynamics, and the Maslov Index. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-11922-4_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11921-7
Online ISBN: 978-3-642-11922-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
